POWER DELIVERY EFFICIENCY: A VALID MEASURE
OF BELT AND TIRE TRACTOR PERFORMANCE
F. M. Zoz, R. J. Turner, L. R. Shell
ABSTRACT. Traction tests comparing rubber belts to rubber tires have generally shown better tractive performance for rubber
belts. However, tests measuring field productivity and fuel consumption on complete vehicles have shown little difference
between rubber belt and rubber tire tractors. Recent tests of both types of tractors by Southwest Texas State University and
the Alberta Farm Machinery Research Centre have used Power Delivery Efficiency, the ratio of drawbar horsepower to input
horsepower, as a measure of overall tractor performance. This article will show why Power Delivery Efficiency is a valid
parameter for making tractor comparisons.
Keywords. Power delivery efficiency, Tractive efficiency, Belt, Tire, Tractor, Traction.
M
any traction performance comparisons have
been made between rubber tires and rubber
belts. Tests using Tractive Efficiency (TE) as
the measure of performance have generally
shown rubber belts to have better performance than rubber
tires. Tests using Power Delivery Efficiency (PDE) as the
measure of performance have shown little difference
between rubber tire and rubber belt equipped tractors. Full
field productivity and fuel–efficiency tests have also shown
little difference between similar rubber belt and rubber tire
tractors. The objectives of this article are: (1) to explain what
PDE is, (2) to show how PDE is different from TE, (3) to show
how PDE is used to measure tractor performance, and (4) to
show that PDE is a valid parameter to use for comparisons
between traction vehicles.
WHAT IS POWER DELIVERY EFFICIENCY?
Power Delivery Efficiency is defined as the ratio of the
delivered drawbar power of a tractor to the vehicle input
power of the tractor. It represents the percentage of power
produced by the engine of a tractor that is available as tractive
power delivered through the drawbar (Shell et al., 1997;
Turner et al., 1997). Tractive Efficiency is defined as the ratio
of output power to input power of a tractive device (ASAE
Standards, 1995). It represents the percentage of power
delivered to a tractive device that is available as tractive
power from the device. PDE includes TE and the efficiencies
of the entire traction vehicle drivetrain from engine to the
Article was submitted for review in April 2000; approved for
publication by the Power & Machinery Division of ASAE in November
2001. Presented at the 1999 ASAE Annual Meeting as Paper No. 991034.
The authors are Frank M. Zoz, ASAE Member Engineer, John Deere
Product Engineering Center, Waterloo, Iowa; Reed J. Turner, ASAE
Member Engineer, Alberta Farm Machinery Research Centre, Lethbridge,
Alberta; Lon R. Shell, ASAE Member, Professor, Department of
Agriculture, Southwest Texas State University, San Marcos, Texas.
Corresponding author: Lon R. Shell, Dept. of Agriculture, Southwest
Texas State University, San Marcos, TX 78666; phone: 512–245–2130;
fax: 512–245–3320; e–mail: [email protected].
drawbar. Because TE does not consider drivetrain and other
losses, it is effectively a subset or component of PDE. When
considering the performance of traction vehicles, PDE gives
a more complete and meaningful understanding of performance differences. Unlike TE, there is not yet a standard
definition for PDE.
PDE is computed by dividing drawbar power by a
specified input power measured at some location behind the
engine. Exactly where this input power is measured may vary
with the specific vehicle. It is advantageous for the input
power to be measured at a location that defines the power
level of the tractor being tested. For many tractors, this is the
Power Take Off (PTO). For vehicles where size is commonly
specified by engine power, such as four–wheel–drive tractors
or tractors without PTOs, engine flywheel power would be
the better measurement. If the power used as the input is
measured at the drive axle, then the result is TE, a component
of PDE. When engine flywheel power or axle power is used
as the input, it is normally measured directly during tractor
comparison testing. When PTO power is used, it is commonly
predicted during tractor comparison testing using laboratory–derived regressions from previously correlated engine
parameters such as engine speed, fuel rack position, and
injector needle lift duration. While power measured at
different locations such as engine flywheel, PTO, transmission output, or drive axles can be used in the PDE calculation,
if two tractors are to be correctly compared to one another,
then the power used for the PDE calculation must be
measured at the same point on each tractor.
TRACTION MECHANICS REVIEW
A review of traction mechanics can help understand how
differences in tractive performance affect PDE. The basic
forces involved in a powered wheel are shown in figure 1.
The torque input (T) develops a gross traction (GT) acting
at the wheel’s loaded radius (Lr). Part of the gross traction is
required to overcome motion resistance (MR), which is the
resistance to the motion of the wheel, including internal and
Transactions of the ASAE
Vol. 45(3): 509–518
E 2002 American Society of Agricultural Engineers ISSN 0001–2351
509
TRACTIVE EFFICIENCY
Va
v
GT= T /Lr
MR= GT – NT
Ws
NT
Vt=ϖ rpm * r / 9.549
m/s
T
r Lr
Ground Line
MR
GT
Ws= Load, static
Wd = Load, dynamic
Lr = Loaded radius, static
r = rolling radius
eh
Wd
Vt = Velocity, theoretical MR = Motion Resistance
Va = Velocity, actual
T = axle torque
GT = Gross Traction (theoretical pull)
NT = Net Traction ( drawbar pull)
Figure 1. Deformable wheel on soft surface.
external forces. The remainder is equal to the net traction
(NT). Dividing by the dynamic load on the wheel (Wd)
results in the following dimensionless relationships:
GT / Wd = Gross Traction Ratio (GTR)
NT / Wd = Net Traction Ratio (NTR)
MR / Wd = Motion Resistance Ratio = GTR – NTR
The theoretical travel speed (Vt) depends upon effective
radius (r) and rotational speed (ù). Input power is the product
of theoretical speed (Vt) and gross traction (GT). Output
power is the product of actual travel speed (Va) and net
traction (NT). Tractive efficiency (TE) is the ratio of output
power to input power:
TE =
=
Net Traction × Actual Speed
Gross Traction × Theoretical Speed
NT
NT Va
Wd Va =  NTR Va 
=
GT
GT Vt
Vt  GTR  Vt 
Wd
(1)
The mechanics of a belt drive mechanism, as shown in
figure 2, are similar to a wheel, but the distribution of the load
is dependent upon vehicle parameters. Location of the
dynamic load resultant, eh (dynamic balance ratio) (Corcoran and Gove, 1985), depends upon static weight distribution
and vehicle weight transfer characteristics.
ϖ
Vt = ϖ rpm * r / 9.549 m/s GT= T/ Lr
Va
MR= GT–NT
NTNT
W1s
W2s W3s
NT
W4s
T
Tractive Efficiency (TE) has been defined as the ratio of
output power to input power of a tractive device. The losses
in output power that cause tractive “inefficiency” come from
both velocity losses and pull losses. The first component, the
velocity losses or loss in travel speed, is correctly called
Travel Reduction, although it is also often referred to as
“slip”. Travel Reduction results from the theoretical travel
speed not being entirely converted to actual speed. This
results from movement within the soil, movement between
the soil surface and the tractive device (a more proper
definition of slip), and movement within the tractive device
itself (tire or lug windup or belt slippage). Each of these
contribute to travel or speed loss. The second component of
tractive inefficiency, the pull loss, is often overlooked. This
is the loss of pull when motion resistance reduces the amount
of gross traction converted to useful output or net traction.
This is especially relevant to belts, where internal losses are
greater than those within tires. On softer soils, internal belt
losses are somewhat compensated for by the lower external
motion resistance that belts have compared to tires.
Figure 3 is a generalized plot of the traction relationships
for radial ply tires from the Brixius (1987) traction equations.
While traction data have been traditionally plotted with
“slip” as the independent variable, it is becoming more
accepted that pull, or net traction, should be the independent
variable, as is shown in figure 3. For a properly ballasted and
inflated farm tire, TE tends to maximize at a Net Traction
Ratio (NTR) of approximately 0.40, as in figure 3. This was
also recognized by Dwyer (1984). Motion resistance tends to
be a linear function of either slip or NTR unless (slip) sinkage
becomes a factor.
The travel and pull losses resulting in tractive inefficiency
do not have official terminology. A simple way to understand
them is to consider a “Velocity Ratio” and “Pull Ratio.”
Equation 1:
 NTR  Va 
TE = 
 
 GTR  Vt 
can be interpreted as a Pull Ratio  NTR  times a Velocity
 GTR 
Va


Ratio   .
 Vt 
Figure 4 shows the Velocity Ratio and Pull Ratio as
functions of NTR. At zero NTR (zero pull), the actual
velocity (Va) is close to the theoretical velocity (Vt),
depending somewhat on the definition of “zero” slip (Dwyer,
1984), and the Velocity Ratio is near unity. As pull increases,
1.00
W5s
Gross Traction Ratio, GTR
0.90
r Lr
Tractive Efficiency Ratio, TE
0.80
MR
eh
Ws = Load, static
Wd = Load, dynamic
Lr = Loaded radius, static
r = Rolling Radius
Wd
Vt = Velocity, theoretical
Va = Velocity, actual
T = axle torque
GT = Gross Traction (theoretical pull)
NT = Net Traction ( drawbar pull)
Ratios
Ground Line
GT
0.70
Net Traction Ratio, NTR
0.60
0.50
MR = Motion
Resistance
0.40
0.30
Travel Reduction Ratio = (1–Va / Vt )
0.20
Motion Resistance Ratio
0.10
= GTR – NTR
0.00
Figure 2. Rubber belt on soft surface.
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Net Traction Ratio
Figure 3. Generalized traction relationships.
510
TRANSACTIONS OF THE ASAE
 NTR Va
TE= 
 
 GTR Vt
TRACTIVE EFFICIENCY PERFORMANCE
COMPARISONS
1.00
0.90
Velocity Ratio =Va / Vt
Tractive Efficiency
Ratio
0.70
0.60
Ratios
Figure 7 shows the tractive performance of 20.8 R42 dual
tires on three surfaces of decreasing firmness. While the peak
TE is reduced as the soil becomes softer and looser, the peak
still occurs at NTR of approximately 0.4 on all soils.
Maximum NTR is also reduced as the soil becomes less firm.
Figure 8 shows the performance of 610 mm wide belts on
the same three soil surfaces. The TE is higher than it was for
the tires, and while it decreases as the soil becomes softer and
looser, it does not decrease as rapidly as it did for the tires.
The peak occurs at a slightly higher NTR than for the tires,
around 0.5, and the belts show a wider range of pull near
maximum efficiency than did the tires.
Pull Ratio = NTR / GTR
0.80
0.50
0.40
0.30
Travel Reduction Ratio = (1– Va / Vt )
0.20
0.10
0.00
0.00
Motion Resistance Ratio = GTR – NTR
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Net Traction Ratio, NTR
Figure 4. Tractive efficiency showing velocity and pull loss components.
travel reduction or slip increases and the Velocity Ratio
decreases, with Velocity Ratio losses reflecting the characteristic shape of the pull–slip curve. At zero NTR, the Pull Ratio
approaches zero (Upadhayay et al., 1988). The difference
between GTR and NTR is motion resistance, which is in the
range of 0.05 to 0.15. Because of motion resistance, NTR can
never equal GTR, so the Pull Ratio can approach but never
reach unity. The overall TE cannot be greater than either the
Pull or Velocity Ratio and reaches a maximum value at NTR
of about 0.4 with radial ply tires. A similar but slightly higher
NTR value exists for belts.
Figure 5 uses field data for radial ply tires in medium
(tilled) tractive conditions to show the actual relationships for
Pull Ratio, Velocity Ratio, and TE shown theoretically in
figure 4. The curves are the result of regression analysis
(Brixius and Wismer, 1978) of the test data. Both velocity
(slip) and pull (motion resistance) losses contribute to overall
tractive (in)efficiency.
Figure 6 shows the data from figure 5 plotted in the more
traditional way with Travel Reduction Ratio as the independent variable. While the information is the same, the effect
of the pull losses and velocity losses cannot be seen as clearly
as in figure 5.
Axle Wt = 8304 kg
POWER DELIVERY EFFICIENCY
Power Delivery Efficiency (PDE) has been defined as the
ratio of drawbar power over vehicle input power, or the
percentage of power produced by the engine of a tractor that
is available as tractive power delivered through the drawbar.
Although most previous tractive performance work has
considered only the difference between axle and drawbar
performance, axle power is not typically the parameter used
for sizing tractors. Tractors are normally sized and purchased
by either engine or PTO power. PDE considers the entire
vehicle from the engine or PTO to the drawbar, including all
hydraulic and drivetrain power losses, while TE considers
only the losses between the axle and the drawbar.
When using PDE as a performance comparison tool, it is
essential that the same point for input power measurements
be used on those tractors being compared. PDE is most
effective as a comparator if the engine flywheel power can be
measured and used in the calculation. Measured engine
flywheel power is used directly in the PDE calculation as
follows:
Tire = 20.8R42 Duals
Pressure = 83 kPa
Surface = Tilled
1.00
0.90
Pull Ratio
Velocity Ratio
0.80
Gross Traction Ratio
Ratios
0.70
Tractive
Efficiency
0.60
0.50
NTR = 0.664(1– exp(–9.8(TRR)))
0.40
SLIP
0.30
Travel Reduction Ratio
0.20
Motion Resistance Ratio
0.10
0.00
0.00
MRR = 0.090 + 0.010(TRR))
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Net Traction Ratio
Figure 5. Velocity and pull losses from actual test data.
Vol. 45(3): 509–518
511
Axle Wt = 8304 kg
Tire = 20.8R42 Duals
Pressure = 83 kPa
Surface = Tilled
1.00
0.90
Tractive Efficiency Ratio
0.80
Net Traction Ratio
Ratios
0.70
0.60
0.50
NTR = 0.664(1– exp(–9.8(TRR)))
0.40
MRR = 0.090 + 0.10(TRR))
0.30
Motion Resistance Ratio
0.20
0.10
0.00
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Travel Reduction Ratio
Figure 6. Traditional travel reduction ratio plot of traction data.
1.00
0.90
Tractive Efficiency Ratio
0.80
Ratios
0.70
0.60
0.50
Subsoiled
0.40
Tilled
Untilled
0.30
0.20
0.10
Travel Reduction Ratio
0.00
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
NET TRACTION RATIO, NTR
Figure 7. Tractive performance of 20.8 R42 dual tires on three surfaces.
1.00
Tractive Efficiency Ratio
0.90
0.80
Ratios
0.70
Subsoiled
plot of field data with Equivalent PTO power calculated from
measured engine power on the horizontal axis and Equivalent
PTO power calculated from a regression on engine speed on
the vertical axis. The good correlation (R2 = 0.98) confirms
the useability of PTO regressions in PDE analysis. While this
example uses only engine speed as the regression variable, if
other parameters are available and used, then the correlation
coefficient and resulting confidence can be improved. As
figure 9 shows, the use of equivalent PTO power introduces
greater variation into the PDE data. Because this lowers the
confidence levels of any resulting conclusions, it is preferable to measure and use engine power where possible.
To use equivalent PTO power, the engine power output
must be kept the same for the drawbar tests as it was for the
PTO tests. Given this, the PDE calculation then becomes:
PDE =
Tilled
0.60
Untilled
0.50
Drawbar Power
Equivalent PTO Power
(3)
0.40
0.30
0.20
Travel Reduction Ratio
0.10
0.00
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Both the available PTO and axle power depend upon
engine power and the losses in the drivetrain and hydraulics.
PTO or transmission drivetrain and hydraulic losses will
reduce power at the PTO or axle respectively.
NET TRACTION RATIO, NTR
PTO Power Regression Compared To PTO Power Derived from Engine Power
Figure 8. Tractive performance of 610 mm belts on three surfaces.
Drawbar Power
Engine Power
(2)
If engine power cannot be measured on a tractor but the
tractor has a PTO, equivalent PTO power can be used for the
PDE calculation. To do this, stationary dynamometer runs
must be made prior to field testing, and data from these runs
must be regressed to determine PTO power as a function of
engine speed and other significant parameters. Equivalent
PTO power can then be predicted during the field tests from
measurements of the parameters used in the regression
(Turner, 1993) and used to calculate PDE. Figure 9 shows a
512
PTO Power Calculated From Engine
Speed by Regression, kW
PDE =
JD 8400T in Primary Tillage in 1997
250
200
150
100
y = 0.9661x + 1.2333
2
R = 0.9822
50
0
0
50
100
150
200
250
PTO Power Calculated From Measured Engine Power, kW
Figure 9. PTO power calculation variations.
TRANSACTIONS OF THE ASAE
PTO power = Engine power – PTO drive loss
PDE PERFORMANCE COMPARISONS
– Hydraulic loss from PTO operation.
Axle power = Engine power – Transmission drive loss
– Hydraulic loss from transmission operation.
Drawbar power = Axle power Ü Tractive Efficiency.
PDE=
=
Drawbar Power
Equivalent PTO Power
Trans. Drive Efficiency × TE
PTO Drive Efficiency
(4)
Hydraulic losses during stationary PTO operation are
relatively constant for any given tractor. Hydraulic losses
during field operations include those necessary for both
tractor and implement operation and can vary widely. While
efforts can be made to limit steering while data are being
taken, power is still required for the steering system itself.
This power may be different during drawbar operations than
when sitting stationary during PTO tests. Because PDE
depends upon transmission and PTO drive efficiencies
(including hydraulic losses) as well as tractive efficiency, any
differences between the stationary and mobile state are taken
into account.
Figure 10 is a PDE performance map for one tractor over
a range of pulls and speeds. The data were measured while
varying the load in selected gears (the near vertical lines), and
while keeping the load constant and varying the gears to
change the travel speed (the horizontal lines). Constant
drawbar power levels are shown by the light gray background
isolines. The numbers to the right of the pull–speed
intersection points show PDE, calculated as the percent of
drawbar power to PTO power. The figure shows the overall
effect of transmission, PTO drive, and tractive efficiencies.
PDE drops off significantly at low pull levels because of the
drop in both drivetrain efficiency and tractive efficiency at
low power levels (the losses remain relatively constant,
becoming a larger percentage as power levels decrease).
Tractive efficiency peaks in the range where pull is 40% to
50% of the tractor weight.
One common comparison of PDE comes from Nebraska
or OECD tests and can serve as an example of how PDE is
determined. These tests show both maximum drawbar and
PTO power for the test tractor. Dividing drawbar power by
PTO power gives a measure of the overall efficiency of power
transmittal on concrete regardless of tractor size or type. The
maximum drawbar power value is usually the one of most
interest. For example, Nebraska Test 1722, Caterpillar
Challenger 75D, shows a maximum PTO power level of
212.01 kW at 2097 engine rpm. Maximum drawbar power at
the same engine rpm occurred in 3rd gear with 189.80 kW.
Dividing 189.80 by 212.01 gives a PDE of 0.895 or 89.5%.
To use Nebraska tests to compare drawbar to PTO power
delivery, it is necessary to assume that engine power output
is the same for each test case. This means the same ambient
conditions for PTO and drawbar tests, as well as the same fuel
temperatures and tractor warmup procedures (same oil
temperatures). Since the concrete track remains a constant in
the tests, useful comparisons can be made between models
from different companies.
PDE calculations from Nebraska tests are usually based
upon a single full load, full power data point. Although field
test data are usually compared over a range of engine speeds,
loads, and gears, the same procedure used in the field can be
applied to Nebraska test data. As an example, figure 11 shows
PTO data from Nebraska Tests for a John Deere 8400
MFWD, plotted as a function of engine speed. The plot shows
the points from the variable load portion of the tests and the
performance runs at reduced engine speeds. Best–fit regressions of PTO power as a function of engine speed are applied
separately to the two portions of the data on either side of the
full governed load point of the engine curve.
Table 1 shows the drawbar data from this Nebraska test.
Equivalent PTO power is calculated for the appropriate
engine speed range using the PTO regression curves from
figure 11. PDE is also calculated for each data point, and the
results are plotted in figure 12. Note that Vehicle Traction
Ratio (VTR) is the ratio of the drawbar pull to the total weight
(total dynamic load) of the vehicle.
Power Delivery Efficiency Map using Percent of PTO Power at Drawbar
(Isolines show Constant Drawbar Power levels)
100 kW
140
33
Drawbar Pull, kN
120
150 kW
200 kW
61
65
65 64 82
72
81
68
67
63
71 75 7174
72
66
67
81
63 66
75 78
74
79
71
81
73
64
74
80 73 76
77 77
68
71
61
67
82 79
76
74
78
62 64
70
75
71
75
79
82
8280
72
79 77
80
75
55
76
75
67
70
78
65
77
77 79
59
70
77
80
78
76
25 kW
78
76
77
78
54
58
65
70
72
74
71
77 75
71
69
57
66
66
67
60
63
59
53
74
67
67
61
59
41 46
48
64
61
57
59
48
61
49
54
32
44
36
43
51
54
24
49
47
34
47
37
45
34
39
32
24
24
10 11
21
21
22
23
15
15
17 21
20
24
12
22
50 kW
100
80
60
40
20
0
0
2
6155
4
6
8
Travel Speed, km/h
10
12
72
71
58
51
47
27
26
28
25
14
Figure 10. Power delivery performance map.
Vol. 45(3): 509–518
513
Nebraska Tractor Test Lab PTO Results
JD 8400 MFWD
250
PTO kW = –0.0009583(rpm)
R
PTO kW
200
2
2
+ 3.9326185(rpm) – 3844.1
= 0.9993
Part Load (linear )
Torque Curve
(Polynomial fit)
150
100
PTO kW = –3.9824(rpm) + 9159.7
2
R = 0.9971
50
0
1800
1900
2000
2100
2200
2300
2400
Engine rpm
Figure 11. PTO power vs. engine speed for John Deere 8400 MFWD.
DB Power
(kW)
Pull
(kN)
Table 1. Nebraska tractor test data, John Deere 8400 MFWD, front engaged.
Speed
Engine
TR
PTO Power
PDE
(km/h)
(rpm)
(%)
(kW)
(DB/PTO)
VTR
Unballasted, 2200 rpm, wt. = 8780 kg
150.84
70.85
118.47
53.06
80.56
35.40
7.66
8.03
8.19
2199
2260
2277
5.04
3.12
2.03
170.62
148.99
91.50
0.884
0.795
0.881
0.823
0.616
0.411
Unballasted, 2000 rpm, wt. = 8780 kg
131.88
85.09
147.38
83.08
156.22
81.23
162.67
75.52
165.31
66.48
165.37
58.46
165.04
51.27
164.08
39.77
5.58
6.39
6.49
7.76
8.95
10.19
11.59
14.85
2258
2154
2070
2001
2006
1996
2001
1999
14.05
9.46
8.75
6.39
4.52
3.65
3.12
2.21
149.81
181.73
191.35
188.44
188.90
187.84
188.44
188.14
0.88
0.811
0.816
0.863
0.875
0.881
0.876
0.872
0.988
0.965
0.943
0.877
0.772
0.679
0.595
0.462
Ballasted, 2000 rpm, wt. = 13,410 kg
121.68
130.07
144.60
125.91
158.43
121.97
163.82
108.67
165.55
95.82
165.57
84.29
164.91
73.90
164.83
65.22
164.22
57.16
163.10
50.31
161.07
38.95
3.36
4.14
4.68
5.42
6.21
7.07
8.03
9.09
10.35
11.67
14.89
2263
2160
2000
1999
1998
1998
2001
2000
2002
1996
1992
9.33
8.7
7.9
5.25
4.05
3.43
2.9
2.45
2.09
1.81
1.26
147.20
180.53
188.29
188.14
188.07
188.07
188.44
188.29
188.51
187.84
187.32
0.826
0.801
0.841
0.871
0.88
0.88
0.875
0.875
0.871
0.868
0.86
0.989
0.958
0.928
0.826
0.729
0.641
0.562
0.496
0.435
0.383
0.296
Ballasted, 2200 rpm, wt. = 13,410 kg
121.18
129.55
142.88
120.26
150.86
101.86
151.27
89.89
151.82
79.00
3.36
4.28
5.33
6.05
6.92
2263
2199
2198
2194
2199
9.4
7.25
4.57
3.7
2.99
147.20
170.62
170.91
172.11
170.62
0.823
0.837
0.883
0.879
0.89
0.985
0.915
0.775
0.684
0.601
Figure 12 also shows the data and fitted curve for a
Caterpillar Challenger 45 rubber belt tractor. This curve was
developed using the same procedure on data obtained from
OECD tests. Here is a PDE comparison on two different types
of tractors having two different power levels, two different
test locations, and using data from both ballasted and
unballasted test setups. While the PTO and drawbar powers
514
are quite different, the PDEs in this example on concrete are
virtually the same.
Valid PDE comparisons using PTO power measurements
require that engine output be the same under the PTO and
drawbar test conditions. In the field, this means careful
control of the variables and/or including them in the
regression analysis for the PTO power calculation. These
TRANSACTIONS OF THE ASAE
PTO Power Delivery Efficiency
Nebraska–OECD Power Delivery Efficiency Comparison
Ratio of Drawbar Power to PTO Power
1.00
0.95
0.90
0.85
0.80
JD 8400 MFWD, Nebr
(Ballasted and Unballasted )
0.75
0.70
Cat 45, OECD Canada
0.65
(Ballasted and Unballasted )
0.60
JD8400 MFWD Nebr
0.55
0.50
0.0
Cat 45 OECD Canada
0.2
0.4
0.6
0.8
1.0
1.2
Vehicle Traction Ratio, VTR
Figure 12. Power delivery efficiency comparison using Nebraska and OECD data.
TRACTIVE EFFICIENCY COMPARED TO
PDE
Comparisons using PDE for the vehicles instead of TE for
their tractive devices can give a better understanding of total
vehicle performance differences. Figures 14 and 15 show a
TE performance comparison for a rubber belt tractor and an
MFWD rubber tire tractor in two soil conditions. The lines
show the regression curve for each case. The TE for the belts
on the rubber belt tractor exceeds that of the tires on the
rubber tire tractor at all pull levels, and the difference
increases as soil conditions deteriorate (secondary tillage).
This suggests that the rubber belt equipped tractor should
show greater efficiency than the rubber tire equipped tractor,
exceeding it in the percent of the engine power delivered to
the drawbar and requiring less fuel for a given area worked.
Figures 16 and 17 show a PDE comparison for the same
set of tests. As expected, PDE is lower than TE for both the
rubber belt and rubber tire tractors because of PTO and
transmission drivetrain losses. While the PDE plots have a
Vol. 45(3): 509–518
wider spread of data points, they show little difference
between the rubber belt tractor and the rubber tire tractor in
the normal range of pull for field operations of 0.3 to
0.5 VTR. In primary tillage, even though the TE was higher
for the rubber belt tractor across the full range of VTR, the
PDE for the rubber belt tractor is lower than the rubber tire
tractor below 0.5 VTR. In the softer secondary tillage, the
PDE of the rubber belt tractor is lower than the rubber tire
tractor below 0.3 VTR and equivalent through about
0.4 VTR. This suggests a different conclusion than that from
the TE data. In percent of available engine power delivered
or in fuel required per area worked, when the tractors were
operating below 0.5 VTR, the rubber belt tractor would at
best be equal to the wheel tractor and could actually be worse
at lower VTR.
Confirmation of the validity of PDE comparisons can be
seen in data from full field productivity and fuel consumption
test comparisons. The full field test procedure, as documented by Turner et al. (1997), involved the uniform tillage
of measured areas of approximately 16 hectares by the
different tractors to be compared. All tractors were operated
similarly, in a manner modeled as closely as possible to the
way a customer would use them. The primary measurements
made were area tilled, fuel consumed, and time to complete
Nebraska Test Comparison JD9400 and Cat 85D
Effect of Engine Power Level Changes on the accuracy of PDE
PTO Power Delivery Efficiency Ratio
examples use only engine rpm in the regressions because the
data came from tests where no other data were available. The
assumption is that major variables such as ambient temperature and fuel temperature were being controlled.
Engine power may vary between the PTO tests and the
drawbar or field tests for reasons such as differing throttle
position, differing fuel blends, or specific design constraints.
An example of the effect of engine power variation on a PDE
comparison using PTO power is shown in figure 13. This
graph shows PDE values using PTO power calculated from
the Nebraska test data on a John Deere 9400 and Caterpillar
85D. Both these tractors have engine derate systems. The
Deere derates during PTO operation. This effectively lowers
the equivalent PTO power in the field and raises the
calculated PDE. The Caterpillar derates in certain gears in the
field. This effectively raises the equivalent PTO power in the
field and lowers the calculated PDE. As can be seen in
figure 13, these power variations make any attempted PDE
comparison meaningless.
1.100
JD9400
Unballasted
1.000
0.900
0.800
Cat 85D
Unballasted
0.700
0.600
0.500
0.000
Cat 85D 1st Gear Derated
Cat 85D 2nd Gear Derated
Cat 85D 3rd Gear Correct
JD9400 Correct
JD9400 PTO Derated
0.200
0.400
0.600
0.800
Vehicle Traction Ratio, VTR
1.000
1.200
Figure 13. Effect of engine power variation on power delivery efficiency
comparison.
515
Belt and Tire Tractive Performance
Primary Tillage
1
TRACTIVE EFFICIENCY
BELT
0.9
0.8
TIRE
Ratios
0.7
0.6
0.5
0.4
0.3
TIRE
0.2
TRAVEL REDUCTION
0.1
BELT
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Vehicle Traction Ratio, VTR
Figure 14. Tractive performance comparison in primary tillage.
Belt and Tire Tractive Performance
Secondary Tillage
1
TRACTIVE EFFICIENCY
0.9
BELT
0.8
Ratios
0.7
TIRE
0.6
0.5
0.4
0.3
TIRE
TRAVEL REDUCTION
0.2
0.1
BELT
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Vehicle Traction Ratio, VTR
Figure 15. Tractive performance comparison in secondary tillage.
the area. Engine power, drawbar power, and PDE measurements were also recorded and averaged during the tests. The
depth of the trailed implement was held constant during the
tests. The width of the implement was set in proportion to the
nominal power level of the tractor under test to ensure that
each tractor would be operating near optimum tractive
efficiency, approximately 0.4 VTR for the rubber tire tractors
and 0.5 VTR for the rubber belt tractors. Steering power
losses were minimized and standardized by using fields of the
same rectangular shape and by lifting the implement out of
the ground for each turn for all tractors.
Figures 18 – 20 show results from a series of these full field
tests that used four different vehicles in two comparison sets:
a 172 kW John Deere 8400 MFWD (tires) compared to a
180 kW John Deere 8400T (rubber belts), and a 157 kW New
Holland Genesis 8970 (tires) compared to a 168 kW
Caterpillar Challenger 55 (rubber belts). The tractors were
516
tested on primary (stubble) and then again on secondary
(fallow) field surfaces. As the figures show, there was little
difference in workrate, specific fuel rate, or PDE between
rubber belt and rubber tire tractors on a given field surface.
The PDE comparison correctly represented what a
customer using the actual machines would have experienced
when considering workrate and fuel rate.
CONCLUSIONS
Power Delivery Efficiency (PDE) can be used to provide
valid, complete vehicle tractor performance comparisons.
When comparing tractors with drivetrain designs that are
significantly different, as is the case of belted versus wheel
tractors, PDE provides more accurate vehicle performance
comparisons than does TE. PDE comparisons show there is
TRANSACTIONS OF THE ASAE
Belted and Tire Vehicle Power Delivery Performance
Primary Tillage
Using PTO Power calculated from engine power
1
POWER DELIVERY EFFICIENCY
0.9
TIRE VEHICLE
0.8
Ratios
0.7
0.6
BELTED VEHICLE
0.5
0.4
0.3
TIRE VEHICLE
0.2
TRAVEL REDUCTION
0.1
BELTED VEHICLE
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Vehicle Traction Ratio, VTR
Figure 16. Power delivery performance comparison in primary tillage.
Belted and Tire Vehicle Power Delivery Performance
Secondary Tillage
1
Using PTO Power calculated from engine power
POWER DELIVERY EFFICIENCY
0.9
BELTED VEHICLE
0.8
Ratios
0.7
0.6
TIRE VEHICLE
0.5
0.4
0.3
TIRE VEHICLE
0.2
TRAVEL REDUCTION
0.1
BELTED VEHICLE
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Vehicle Traction Ratio, VTR
Figure 17. Power delivery performance comparison in secondary tillage.
0.30
12.0
0.25
9.05
8.18
8.0
8.18
7.81 7.56
7.23
6.50
5.63
6.0
4.0
0.20
0.20 0.19
.19
.18
.17
.15
0.15 0.15
0.15
0.10
0.05
2.0
0.00
0.0
Primary
Deere 8400T
Fuelrate (Ha/L)
Workrate (Ha/hr)
10.0
Deere 8400
Secondary
Cat 55
NH 8970
Primary
Secondary
Deere 8400T Deere 8400 Cat 55
NH 8970
Figure 18. Full field test results showing work rate.
Figure 19. Full field test results showing fuel rate.
less overall difference in performance between belted and
rubber–tired tractors than would be implied by TE comparisons alone. Computing PDE using measured engine flywheel
power yields data with the least amount of scatter. When
engine power cannot be measured, it can be computed from
engine speed using laboratory–derived PTO power regressions. This will, however, increase variability in PDE data
because the available engine power is dependent upon a
Vol. 45(3): 509–518
517
REFERENCES
Power Delivery Efficiency
1.00
0.80
.76 .77
0.70
.74
0.66
.68
0.70
0.66
0.60
0.40
0.20
0.00
Primary
Deere 8400T
Deere 8400
Secondary
Cat 55
NH 8970
Figure 20. Full field test results showing power delivery efficiency.
number of field variables. Tightly controlling such variables
or including them in the PTO performance regressions can
reduce this variability.
518
ASAE Standards. 1995. S296.4. Uniform terminology for traction
of agricultural tractors, self–propelled implements, and other
traction and transport devices. St. Joseph, Mich.: ASAE.
Brixius, W. W. 1987. Traction prediction equations for bias ply
tires. ASAE Paper No. 871622. St. Joseph, Mich.: ASAE.
Brixius, W. W., and R. D. Wismer. 1978. The role of slip in traction.
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Dwyer, M. J. 1984. The tractive performance of wheeled vehicles. J.
Terramechanics 21(1): 19–34.
Shell, L. R., F. Zoz, and R. J. Turner. 1997. Field performance of
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Traction in Agricultural Vehicles, 65–73. SAE SP–1291.
Warrendale, Pa.: Society of Automotive Engineers.
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performance in the field. ASAE Paper No. 931574. St. Joseph,
Mich.: ASAE.
Turner, R. J., L. R. Shell, and F. Zoz. 1997. Field performance of
rubber belt and MFWD tractors in Southern Alberta soils. In
Belt and Tire Traction in Agricultural Vehicles, 75–85. SAE
SP–1291. Warrendale, Pa.: Society of Automotive Engineers.
Upadhyaya, S. K., W. J. Chancellor, D. Wulfsohn, and J. L.
Glancey. 1988. Sources of variability in traction data. J.
Terramechanics 25(4): 249–272.
TRANSACTIONS OF THE ASAE